Farm:
-event unit is a random drop from maps
-later/costlier maps have higher drop rate (typically 50/5 = 25%, 70/7 = 50%)
-4 maps + 1 X map + 1 G map, easiest event type to beat, but getting the best possible unit is random and spending SCs does not guarantee the best unit (such as Charlotte's ungodly low mincost/SU rates)

Star:
-event rewarded only at the end of the event based on how many stars you have
-more stars = cheaper cost/higher skill
-usually 8+ maps with 2 X maps and 2 G maps, hardest event to clear but easiest type of unit to max since maps only need to be 3*'d once to count

Collection:
-collect X amount of drops, later/costlier maps drop more items
-more drops = cheaper cost/higher SU
-usually same number of maps as Star type, difficulty is easier than Star but harder than Farm, amount of SCs to max unit is the largest, but type of unit is usually worth maxing